Trace formula on a Euclidean surface with conical singularities (Q1565928)

The author establishes a trace formula on an Euclidean surface \(M\) with a finite number of conical singularities situated at the points \( p _{1}, \dots , p _{N}\). The first problem to consider in this context is that of propagation of singularities for solutions of the associated wave operator. For the behaviour near a singularity the author relies mainly on the classical paper of \textit{J. Cheeger} and \textit{M. Taylor} [Commun. Pure Appl. Math. 35, 275--331, 487--529 (1982; Zbl 0526.58049, Zbl 0532.58032)]. The main result is that if we denote by \(U(t)\) the operator \(U(t) = \exp [ \text{it} \sqrt{\Delta }]\), then the singular support of the trace of the distribution \(U(t)\) is contained in the length spectrum of \(M\), i.e., the Poisson relation is valid.